1. Field of the Invention
The present invention relates to a position control system for a servomotor or the like, and more particularly to a position control system for precisely controlling fine positioning operation without lowering speed gain.
2. Description of the Related Art
Positioning operation in a numerical control apparatus or the like requires that a movable member be precisely responsive to a fine positioning command. A control system for a servomotor which effects such positioning is illustrated in FIG. 5. Denoted at 11 is an arithmetic unit for adding a position command 21 and subtracting a position feedback signal 22. A converter 12 with a position gain K converts the position command issued from the arithmetic unit 11 to a speed command (u(s)) 23. An arithmetic unit 13 issues a signal indicating the difference between the speed command 23 and a speed feedback signal 20. An integrator 14 with an integration constant k1 integrates the speed command. Designated at 15 is an arithmetic unit for issuing a signal representing the difference between a torque command 18 from the integrator 14 and a torque feedback command which is produced by multiplying a speed feedback signal 20 by a proportional gain 19. A current control circuit 16 issues a current dependent on the torque command. The reference numeral 17 represents a servomotor. K.sub.t indicates a torque constant, J.sub.m the inertia of the servomotor, 24 a speed output from the servomotor, and 25 a position output from the servomotor. The speed output 24 is fed back directly to the arithmetic unit 13 and also fed back to the arithmetic unit 15 after being multiplied by a proportional gain k2. The position output 25 of the servomotor is fed back to the arithmetic unit 11.
Operation of the position control system thus constructed is shown in FIG. 6. The graph of FIG. 6 has a horizontal axis indicating a movement command in a unit of 1 .mu.m and a vertical axis representing actual movement of a mechanical movable member in a unit of 1 .mu.m. Ideally, a mechanical movable member would move precisely 1 .mu.m each time a command for 1 .mu.m is applied, as indicated by the straight line M1.
Actually, however, as indicated by the polygonal line M2, a mechanical movable member moves 0.2 .mu.m at a time in response to a command for 1 .mu.m and moves 1.8 .mu.m at a time in response to the next command for 1 .mu.m, for example, and hence does not move in exact response to applied commands. Thus, the mechanical movement is polygonal due to the so-called stick/slip phenomenon. This phenomenon is responsible for a reduction in the accuracy of actual operation of the mechanical movable member and for a poor finishing surface.
The causes of such undesirable conditions will be analyzed below. FIG. 7 shows the torque command illustrated in FIG. 5. The graph of FIG. 7 has a horizontal axis indicative of time (t) and a vertical axis of torque (T). When a position command 21 for 1 .mu.m is applied, the torque command 19 issued from the integrator 14 of FIG. 5 increases along a straight line C1 as shown in FIG. 7. When the torque exceeds a static friction torque C3, the servomotor 17 starts rotating. There is a considerable period of time before a position output is actually fed back. During that period of time, the torque command increases. When the servomotor starts to rotate, the servomotor moves beyond the command value since the dynamic friction torque is much smaller than the static friction torque. As a result, the amount of movement when a next command for 1 .mu.m is applied becomes smaller than 1 .mu.m.
To solve the above problem, the integration constant k1 of the integrator 14 shown in FIG. 5 may be made small to cause the torque to increase along a curve C2 as shown in FIG. 7, so that the torque increases more gradually. However, such a solution is still problematic in that when the position command is large, the response of the entire system is slow.